Endo Chaos (2009)

An audio-visual simulation of a chaotic attractor seen from an endo-perspective

by Hans H. Diebner

Hans H. Diebner: Endo Chaos. Screenshots 2009.

This simulation of a chaotic dynamics in phase space allows for a view from within onto the attractor - here the well-known Rössler attractor. Very much like on a roller coaster the recipients fly on a chaotic path through the night sky above the antarctica. An immersive feeling appears and one starts to grasp the meaning of strangness of the chaotic attractor. The upright position of the spectator is defined through the converging manifold in phase space. This manifold is a toplogical structure of the space orthogonal to the attractor, which in fact gives the chaotic formation its name. This is because every point on the converging manifold outside the attractor converges towards the attractor under the impact of the given dynamics. Intuitively this direction in space is associated with gravity.

Within the attractor the dynamics is governed by a diverging manifold. Neighboring states on this manifold exponentially drift away from each other under the impact of the dynamics. This is indeed the defining characteristic of a chaotic dynamics. Because of this exponential divergence the system is unpredictable. A small unavoidable uncertainty is quickly amplified. Within our metaphor of a roller coaster, the diverging manifold constitutes the lateral direction and is intuitively associated with the centrifugal force.

Both manifolds form very complex twisted Möbius-like bands. A Möbius band is a so called non-orientable topological structure. It has only one side which is, so to say, inside and outside at the same time. After a couple of rounds on the roller coaster through phase space, the upright direction flips repeatedly upside-down with respect to the external world.


  1. TRANSITION - knowledge through performance in art and science. Hanse-Wissenschaftskolleg Delmenhorst from 25.10.--30.11.2012.
  2. INM@Night of Museums in Frankfurt upon Main on Sat. 07 May 2011. On the occassion of the "Night of the Museums" all users of the cultural bunker at Schmickstraße 18 (cultural bunker in Frankfurt's East harbor) joint to organize a common programme for "The Night".
  3. New media make sense | Context INM: performative science and vireality An exhibition within the scope of "Forum Science and Art" of the HMWK-Hessian Ministery for Science and Art. Curated by Michael Klein and Hans H. Diebner, Institute for New Media, Frankfurt upon Main. Duration: 9 March - 16 April, 2011. Venue: HMWK Wiesbaden Rheinstr. 23-25. Vernissage: 8 March, 2011, 19.30h.